Hydrostatic Pore Pressure Research Articles

Consolidation responses of delipidized articular cartilage

Objective. To determine the role of articular cartilage lipids in its load-bearing function. Design. Normal and delipidised, bovine articular cartilage specimens were statically loaded and both the hydrostatic excess pore pressure and creep strain were measured. From this the compression stiffness of the skeletal structures of both types of matrices was determined. Background. It has been hypothesized that surfactant injection could relief osteoarthritis, but there is no study in the literature relating to the influence of lipids, the main ingredients of such products, on cartilage load-carriage. Methods. Articular cartilage specimens were obtained from the patellar grooves of 2–3 year old bovine animals. When required specimen delipidization was carried out using chloroform/methanol rinsing. Both normal and delipidised samples were loaded in the consolidometer and the hydrostatic excess pore pressure and strain were measured. Results. The transient patterns of the hydrostatic excess pore pressure were similar for both types of tissue, with a relatively insignificant increase of 2% in the maximum hydrostatic excess pore pressure of the delipidized samples relative to the normal intact specimens. The maximum creep strain of the delipidised specimens decreased by 10% on average relative to their normal intact counterparts, thereby indicating that delipidization causes stiffening of the cartilage matrix. Conclusion. The delipidized fluid-saturated articular cartilage is stiffer than its intact counterpart with consequence for cartilage compliance during function. Relevance Because osteoarthritis can be accompanied by lipid loss in cartilage, this study contributes to the further understanding of the disease with potential benefit for treatment.

Spatial heterogeneity of tectonic stress and friction in the crust

The complex geometry of faults, seismicity, and diversity of earthquake mechanisms suggest that the stress and strength in Earth's crust are spatially heterogeneous. We investigated the degree of heterogeneity using the following two end‐member models. In one end‐member model, we assumed that the orientation of stress is uniform in the crust as is assumed in many stress inversion studies. In this model, the variability of earthquake mechanisms means that friction during faulting must vary for each event. We computed friction μ from the ratio of the resolved shear stress to the effective normal stress on the fault plane with the assumption of hydrostatic pore pressure. The values of μ vary over a large range from 0 to 1.5. In the other extreme model we assumed optimally oriented slip and a constant μ = 0.6, as is suggested by Byerlee's law, for all the earthquakes, and determined the local stress orientation for each earthquake. The orientation of the stress changes drastically from one earthquake to another, and the assumption of uniform stress field commonly used in stress inversion is not warranted. An important conclusion is that a regionally uniform stress field and constant friction on optimally oriented faults are mutually exclusive. The actual situation in the crust is most likely to be intermediate between these two end‐member models. From the existing data alone, we cannot determine the degree of heterogeneity uniquely, but both μ and the local stress field near earthquake faults are likely to vary substantially, and studies on earthquake rupture dynamics must take these heterogeneities into consideration.

DETECTING OVERPRESSURE USING POROSITY-BASED TECHNIQUES IN THE CARNARVON BASIN, AUSTRALIA

Overpressure has been encountered in many wells drilled in the Carnarvon Basin. Sonic logs are used to estimate pore pressure in shales in the Carnarvon Basin using the Eaton and equivalent depth methods of estimating pore pressure from velocity data with reference to a normal compaction trend. The crux of pore pressure estimation from the sonic log lies in the determination of the normal compaction trend, i.e. the acoustic travel time (Δt)/depth (z) trend for normally pressured sediments. The normal compaction trend for shales in the Carnarvon Basin was established by fitting an Athy-type exponential relationship to edited sonic log data, and is: Δt = 225 + 391exp(-0.00103z) Vertical stress estimates are also needed for the Eaton and equivalent depth methods used herein. A vertical stress (σv) relationship was obtained by fitting a regression line to vertical stress estimates from the density log, and is: σv = 0.0131 z1.0642 The Eaton and equivalent depth methods yield similar pressure estimates. However, the equivalent depth method can only be applied over a limited range of acoustic travel times, a limitation that does not apply to the Eaton method. The pressure estimates from the Eaton method were compared to pressures measured by direct pressure tests in adjacent permeable units. There is a good correlation between Eaton and test pressures in normally pressured intervals in three wells and overpressured intervals in two wells. Eaton pressure estimates underestimate overpressured direct pressure measurements in four wells by up to 13 MPa. This is consistent with overpressure being generated (at least in part) by a fluid expansion mechanism or lateral transfer of overpressure. The Eaton pressures in one well are, on average, 11 MPa lower than hydrostatic pore pressure recorded in direct pressure measurements below the Muderong Shale. The sediments in this well appear to be overcompacted due to exhumation. Mud weights can be used as a proxy for pore pressure in shales where direct pressure measurements are not available in the adjacent sandstones. The Eaton pressure estimates are consistent with mud weight in the Gearle Siltstone and Muderong Shale in 4 of the 8 wells studied. The Eaton pressures are on average 10 Mpa in excess of mud weight in the Muderong Shale and Gearle Siltstone in three wells. It is unclear whether the predicted Eaton pressures in these three wells accurately reflect pore pressure (i.e. the mud weights do not accurately reflect pore pressure), or whether they are influenced by changes in shale mineralogy (because the gamma ray filter does not differentiate between shale mineralogy).

Elastohydrodynamic lubrication of faults

The heat flow paradox provides evidence that a dynamic weakening mechanism may be important in understanding fault friction and rupture. We present here a specific model for dynamic velocity weakening that uses the mechanics of well‐studied industrial bearings to explain fault zone processes. An elevated fluid pressure is generated in a thin film of viscous fluid that is sheared between nearly parallel surface. This lubrication pressure supports part of the load, therefore reducing the normal stress and associated friction across the gap. The pressure also elastically deforms the wall rock. The model is parameterized using the Sommerfeld number, which is a measure of the lubrication pressure normalized by the lithostatic load. For typical values of the material properties, slip distance and velocity, the Sommerfeld number suggests that lubrication is an important process. If the lubrication length scales as the slip distance in an earthquake, the frictional stress during dynamically lubricated large earthquakes is 30% less than the friction with only hydrostatic pore pressure. Elastohydrodynamic lubrication also predicts a decrease in high‐frequency (>1 Hz) radiation above a critical slip distance of a few meters. This prediction is well matched by the strong motion data from the 1999 Taiwan earthquake. The observed 2 orders of magnitude variation in scaled radiated energy between small (Mw < 4) and large earthquakes (Mw > 6) is also predicted by the lubrication model.

Implications of hydrostatic pore pressures and high crustal strength for the deformation of intraplate lithosphere

Observations from deep boreholes at several locations worldwide indicate that (i) hydrostatic pore pressures persist to depths of as much as 12km in the upper crust, (ii) the brittle crust is in a state of failure equilibrium according to Coulomb frictional-failure theory, and (iii) bulk permeability is high — 10−17–10−16m2 — apparently due to fluid flow along critically stressed faults. As a result of these factors, the brittle crust is stronger than it would be under near-lithostatic pore pressure conditions.This result provides a constraint on models of lithospheric deformation. Postulating that the upper and lower crust and lithospheric mantle are totally coupled and that the total strength of the lithosphere is equal to the magnitude of tectonic driving forces (∼3×1012Nm−1), we have calculated lithospheric strain rates under representative thermal and rheological conditions such that the integrated differential stress over the entire thickness of the lithosphere equals the plate driving force. For a strike-slip stress state and surface heat flow of 60±6mWm−2, average strain rates are approximately 10−18s−1 under hydrostatic upper crustal pore pressure conditions, and approximately 10−15s−1 under near-lithostatic pore pressures. The latter strain rates are higher than either observed geodetically using very long baseline interferometry (VLBI), or estimated on the basis of plate tectonic reconstructions. Hence we argue that hydrostatic upper crustal pore pressures enable lithospheric plates to behave rigidly over time scales of tens to hundreds of millions of years.

Fault strength and transpressional tectonics along the Castle Mountain strike-slip fault, southern Alaska

Analyses of structures along the Castle Mountain fault reveal the mechanical relations and relative timing of orogen-parallel strike-slip faulting to distributed wrenching and shortening and to plate motion in the southern Alaskan transpressive margin. The Castle Mountain fault is a >200-km- long, orogen-parallel, right-lateral seismogenic fault in the southern Alaskan plate margin. Exposures of the fault in the study area have been exhumed from 3−4 km depth and ∼80 °C. Moment tensor summations and stress inversions of slip data from fault networks within 400 m of the Castle Mountain fault and analyses of structures in forearc deposits 2−4 km from the fault yield maximum incremental shortening and maximum compressive stress (σ 1 ) axes that are subhorizontal and trend ∼325°. This trend is close to the 340° North American–Pacific plate convergence direction. The inferred σ 1 makes a 70°−80° angle with the ∼070°-striking Castle Mountain fault, indicating that the fault slips at a lower shear stress than predicted by laboratory rock friction experiments if hydrostatic pore pressure exists in the fault (i.e., coefficient of friction ∼0.85, Byerlee9s Law). The forearc structures record coaxial strain and apparently remain in their formative orientations, showing that previously documented distributed shearing in the form of vertical-axis block rotations in the forearc ceased prior to formation of the structures in late Oligocene time. The mechanical weakness of the Castle Mountain fault probably results in part from its clay- rich gouge, which averages about 43 wt% clay phases. However, the gouge composition does not account for slip in response to σ 1 at 70°−80° to the fault. Another mechanism, such as elevated pore pressure, further weakens the fault and enables it to slip right laterally in response to the small component of oblique motion across the plate boundary. Upon its inception in early Tertiary time, the fault could not have formed a >200-km-long planar zone of low-friction clay-rich gouge or elevated pore pressure; thus, the mechanisms that weaken it must have developed over time. The distributed shearing in the forearc may have ended in response to the weakening and localization of dextral slip onto the Castle Mountain fault.

Predictive rheological models for the consolidation behaviour of articular cartilage under static loading.

This paper evaluates an existing rheological model of articular cartilage and explores the representative capacity of other phenomenological models of the tissue's matrix within the framework of mechanical consolidation. A unique feature is the introduction of a swelling element in tandem with 'fluid-filled' hyperelastic rheological elements to predict the transient load-induced behaviour of the tissue and evaluate the role of swelling in determining its load-carriage mechanism. The rheological models proposed have been used to predict the dependence of the one-dimensional consolidation response of the articular cartilage matrix, and the results obtained have been compared with published experimental results. This comparison demonstrates that the hydrostatic excess pore pressure, especially in the initial stages of deformation cannot be predicted without an adequate representation of swelling and its non-linear interaction with mechanical governing parameters such as permeability and stiffness.

Causes and mobility of large volcanic landslides: application to Tenerife, Canary Islands

Giant volcanic landslides are one of the most hazardous geological processes due to their volume and velocity. Since the 1980 eruption and associated debris avalanche of Mount St. Helens hundreds of similar events have been recognised worldwide both on continental volcanoes and volcanic oceanic islands. However, the causes and mobility of these enormous mass movements remain unresolved. Tenerife exhibits three voluminous subaerial valleys and a wide offshore apron of landslide debris produced by recurrent flank failures with ages ranging from Upper Pliocene to Middle Pleistocene. We have selected the La Orotava landslide for analysis of its causes and mobility using a variety of simple numerical models. First, the causes of the landslide have been evaluated using Limit Equilibrium Method and 2D Finite Difference techniques. Conventional parameters including hydrostatic pore pressure and material strength properties, together with three external processes, dike intrusion, caldera collapse and seismicity, have been incorporated into the stability models. The results indicate that each of the external mechanism studied is capable of initiating slope failures. However, we propose that a combination of these processes may be the most probable cause for giant volcanic landslides. Second, we have analysed the runout distance of the landslide using a simple model treating both the subaerial and submarine parts of the sliding path. The effect of the friction coefficient, drag forces and hydroplaning has been incorporated into the model. The results indicate that hydroplaning particularly can significantly increase the mobility of the landslide, which may reach runout distances greater than 70km. The models presented are not considered definite and have mainly a conceptual purpose. However, they provide a physical basis from which to better interpret these complex geologic phenomena and should be taken into account in the prediction of future events and the assessment of landslide related hazards.

Post glacial lithospheric flexure and induced stresses and pore pressure changes in the northern North Sea

We have compiled data on the least principal stress, overburden, pore pressure and stress orientation for 92 wells in the northern North Sea. These data show that the least principal stress is close to the overburden in the Tampen Spur indicating high horizontal stress in this area. Closer to the coast, i.e. east of the Viking Graben the least principal stress drops significantly. Along with this spatial change in stress magnitudes, the orientation of the maximum horizontal stress rotates from ≈100° in the Tampen Spur to ≈80° around block 35/9. Analytical and numerical models of plate flexure suggest that these observed lateral stress variations are the result of deglaciation, superimposed on a regional stress field dominated by ridge push.The pore pressure in the northern North Sea roughly follows the stress trend, i.e. high overpressures where horizontal stresses are high (Tampen Spur) and close to hydrostatic pore pressures east of the Viking Graben where stresses are decreased. This close relationship of pore pressure and horizontal stress suggests that they have the same source. We have modeled the pore pressure change expected from the poroelastic response to deglaciation. The results show that strong overpressures in the Tampen Spur appear to be caused only partly by deglaciation and flexure. Other sources of overpressure, such as compaction disequilibrium also play an important role.

Effects of pore pressure on compressional wave attenuation in a young oceanic basalt

Laboratory data are reported for ultrasonic compressional wave attenuation (αp) as a function of pore pressure in a Juan de Fuca Ridge dredge basalt. Four experiments have been made to determine the relationships between attenuation and quality factor (Qp) and confining and pore pressures in the shallow ocean crust. Attenuation was measured at 1) a constant differential pressure of 40 MPa; 2) confining pressures to 120 MPa and atmospheric pore pressures; 3) a constant confining pressure of 50 MPa while varying pore pressures; 4) a constant confining pressure of 100 MPa while varying pore pressures. For atmospheric pore pressures, αp ranges from 1.64 dB/cm to 7.08 dB/cm (Qp = 24 to 10). In addition, attenuation increases systematically with increasing pore pressure and decreasing differential pressure (confining pressure ‐ pore pressure). Results from DSDP and ODP downhole packer experiments suggest that the hydrostatic pore pressure regime may best approximate in situ conditions for young oceanic crust. Hydrostatic pore pressures (@ 5000 meters depth) reduce Qp as much as 35% from normal atmospheric pressure conditions; therefore, pore pressures generated in the upper oceanic crust may be responsible in part for the observed low seismic Qp within layer 2A. Qp measurements at elevated pore pressures agree well with seismic Qp data.

Experimental factors governing the internal stress state of the intervertebral disc

This paper presents an experimental study of the response of the intervertebral disc to short-term static-axial loading within the conceptual framework of mechanical consolidation as applied to swelling materials. An experimental technique developed previously for articular cartilage was used to load the disc in compression and measure simultaneously the matrix internal excess pore pressure under both radially constrained and radially unconstrained conditions. Specifically the short-term pattern of development of the hydrostatic excess pore pressure was investigated. The average ratio of the maximum excess pore pressure u i to the nominal applied stress for unconstrained loading was approximately 1.9 while for constrained loading it was about 1.4. This behaviour is interpreted in terms of the generation of a pore pressure in the nucleus which reflects a non-uniform partitioning of the applied load across the inhomogeneous structure of the disc. These results provide a quantitative insight into the role that physico-chemically generated swelling plays in determining the internal mechanical response of the disc to an externally applied load and suggest a quantitative means of investigating the important influence of degenerative changes on the internal stress state of the disc without needing to pierce the annular wall in order to insert a pressure sensing device.

Injection‐induced earthquakes and crustal stress at 9 km depth at the KTB deep drilling site, Germany

A fluid injection‐induced seismicity experiment was conducted in the German Continental Deep Drilling Program (KTB) main borehole at 9.1 km depth (in situ temperature of 260°C) to extend knowledge about stress magnitudes and brittle faulting to depths and temperatures approaching the brittle‐ductile transition. Almost 400 microearthquakes were induced at an average depth of 8.8 km by injection of KBr/KCl brine into a ∼70 m open hole section near the bottom of the borehole. Although most focal plane mechanisms were poorly constrained due to the very small size of the induced earthquakes, several different clusters of microearthquakes with distinct mechanisms were defined. Most of the microearthquakes for which focal plane mechanisms were determined were strike‐slip events with a NNW trending P axis, essentially parallel to the direction of maximum horizontal compression observed in the borehole. The largest induced earthquake, M 1.2, occurred 18 hours after injection was started. This event was a strike‐slip/reverse faulting event which also had a NNW trending P axis. Utilization of a precise relative location technique indicates that many of microearthquakes occurred relatively far (50–100 m) from the well bore. Modeling of the pore pressure disturbance caused by injection suggests that many of the earthquakes were induced by extremely small pore pressure perturbations (<1 MPa) less than 1% greater than the ambient, approximately hydrostatic pore pressure at depth. Thus it is apparent that there are critically stressed, permeable fault zones in the crust, even at great depth and temperature. A frictional analysis of the focal plane mechanisms of the induced microearthquakes indicates that fault slip is consistent with the stress magnitudes and orientations determined in situ at depths to 7.7 km in the borehole and relatively high coefficients of friction (∼0.6–0.7) reported by Brudy et al. [this issue]. This and the observation that very small pore pressure perturbations were able to trigger seismicity appear to confirm the hypothesis that “Byerlee's law” (i.e., that differential stresses in situ are limited by the frictional strength of well‐oriented, preexisting faults) is valid to great crustal depth and that the crust is in brittle failure equilibrium at depths and temperatures approaching the brittle‐ductile transition, even in this relatively stable intraplate area.

The stress field in the Rhine Graben area inferred from earthquake focal mechanisms and estimation of frictional parameters

Altogether 98 focal mechanisms of micro to moderate earthquakes (ML = 0.5−5.9) have been used to analyze the state of stress in the Rhine Graben and adjacent areas. Due to dense networks in the investigated area fault plane solutions determined by the first motion method can be fixed with an accuracy better than 10°. The majority of the focal mechanisms is characterized by strike-slip and normal faulting movements; only a few events are of reverse faulting type.To calculate the orientations of the principal stress axes and the shape of the stress tensor we applied the inversion method of Gephart and Forsyth (1984) to three subsets of the data, each of which has been chosen taking into account the local tectonic units (northern Alpine foreland, southern Rhine Graben, northern Rhine Graben including Rhenish Massif and lower Rhine Embayment). For all of the data subsets, the inversions revealed a stable axis of minimum principal stress σ3, oriented horizontally to subhorizontally and striking in a WSW-ENE to SW-NE direction. The azimuth of σ1, the maximum principal stress, is about 150°. However, the confidence regions show that horizontal and vertical orientations of σ1, as well as orientations in between, are of the same probability. Therefore, an unequivocal distinction between strike-slip and extensional regimes is not possible. When comparing the results from the data subsets, a slight counterclockwise rotation from south to north of about 30° of the σ1−σ2 plane plane as well as of the direction of σ3, can be observed. The relative stress magnitude R (R = (σ2 − σ1)/(σ3 − σ1)) has a value of about 0.5 for all subsets, indicating that for the deviatoric part of the stress tensor, σ1 and σ3 are of the same magnitude but of opposite sign. The directions of the horizontal stresses, SHmax and Shmin, inferred from the analysis of focal mechanisms are in good agreement with the general features for western Europe in the European Stress Map.More detailed investigations have been performed for the southern Rhine Graben area. A division into an upper crustal (<15 km) and a lower crustal (>15 km) dataset makes possible the resolution of an individual stress regime for each subset: a strike-slip regime for the upper and an extensional regime for the lower crust, with the same azimuths of the principal stress axes for both depth ranges. Such a change of the stress tensor with depth fits into the tectonic model of detachment zones in the lower crust in the northern front of the Alps, a detachment caused by south-plunging subduction of the European plate beneath the Alps and the Adriatic plate.On the basis of the resolved orientations of the principal stress axes and the shape of the stress tensor, we furthermore estimated absolute stress magnitudes and the ranges of frictional parameters acting on the individual faults. Assuming hydrostatic pore pressure on the faults, frictional coefficients between 0.10 and 0.64 are required to enable slip. On the other hand, when the frictional coefficient has been fixed to 0.65, the required pore pressure values range from 0.38 to 0.62 of lithostatic with an average of 0.48. The absolute stress magnitudes inferred from the analysis of the focal mechanisms compare favourably with the in-situ measurements of absolute stresses from the KTB borehole at Windischeschenbach (German continental deep drilling program).

Frictional coefficient on faults in a seismogenic region inferred from earthquake mechanism solutions

The coefficient of friction associated with faults in a seismogenic region is inferred from numerous focal mechanism solutions. Earthquake slip can occur on a favorably oriented fault plane when preexisting fault planes are oriented in various directions. The fault plane is thought to be selected when the Coulomb failure stress given by σf=τ − μ(σn − p) − S0 has a maximum value along a slip direction on the plane. Here, τ is the shear stress, μ is the coefficient of friction, σn is the normal stress, p is the pore pressure, and S0 is the cohesion. Consequently, the geometry of the plane and the slip direction include information concerning the coefficient of friction for the faults. In the present paper the coefficient of friction is inferred from the distribution of P axis orientations, assuming hydrostatic pore pressure. The method is very simple and has the advantage that the results obtained do not depend on pore pressure, when pore pressure is not proportional to the normal stress. Observed distributions of P axis azimuths and plunges display a very narrow peak having a width of about 20°. The coefficient of friction on the faults can then be estimated from the width to be less than or equal to μ = 0.2. When the stress is balanced by friction, the shear stress can be calculated. Here, the shear stress (in megapascals) has a value of 4.0z, where z is the depth (in kilometers), under the assumption of hydrostatic pore pressure and a coefficient of friction of 0.2. The value obtained for the coefficient of friction is very small compared with those derived from laboratory frictional experiments. It is thought that this small value of μ is attributed to the friction itself, when pore pressure is not proportional to the normal stress.

Biomechanics of load-bearing of the intervertebral disc: an experimental and finite element model

This paper presents an experimental and finite element study of the biomechanical response of the intervertebral disc to static-axial loading in which classical consolidation theory was used to analyse its time-dependent response. A newly developed experimental technique was employed to load the disc in compression and measure simultaneously the matrix internal pressure and creep strain for the full consolidation process. It is shown that, upon loading, the disc develops a maximum hydrostatic excess pore pressure which gradually decays as water is exuded from the matrix. During this decay process, the applied load is progressively transferred to the solid components of the matrix until the load is borne in full by the solid at the end of consolidation. Material properties for the tissue were then obtained from the experimental stress-strain data and used in the finite element study in the development of a finite element solution based on Biot's theory of coupled solid-fluid interaction. An axisymmetric formulation was employed and the disc modelled as an anisotropic, non-linear poroelastic solid. A sensitivity analysis of the material properties for the structural components of the disc was carried out and the biomechanical response to compressive loading evaluated and compared to experimental data. The results show that the matrix permeability plays a significant role in determining the transient response of the tissue. Annualr disruptions of the disc were shown to result in an increase in the nuclear principal stresses suggesting that disrupted regions of the annulus fibrosus play a reduced role in load bearing.

Generation and maintenance of abnormal fluid pressures beneath a ramping thrust sheet: Isotropic permeability experiments

We have investigated the mechanisms responsible for the evolution of excess pore pressures within and beneath a ramping thrust sheet (i.e. fluid flow, porosity compression, and thermal expansion of water) and the sensitivity of pore pressure to a variety of physical parameters (e.g. permeability, thrust sheet velocity, heat flux). Coupled pore pressure and temperature equations were solved numerically in two dimensions using a generalized hydrostratigraphy of North American thrust belts. Because of the lack of either symmetry or a steady-state in this problem, both deposition and thrust loading stages were simulated. The dominant mechanisms controlling pore pressure evolution were fluid flow and compression of pore space by vertical loading; thermal expansion of the fluids was found to be insignificant in generating excess pore pressures at common thrust loading rates. The results indicate that it is possible to generate high pore pressure to lithostatic pressure ratios (λ) within thrust sheets by depositional loading prior to thrusting. High values of λ are generated and maintained during thrust loading for reasonable assumptions about the conditions thought to have existed in thrust belts. Values of λ were not constant throughout the model. The highest λ values tended to concentrate near the surface of the model and within and below the toe of the thrust sheet. The magnitude and distribution of excess pore pressures and λ values were found to be especially sensitive to variations in permeability. Excess pore pressure generation by compression exceeded pore pressure dissipation by fluid flow for permeabilities less than approximately 10 −16 m 2; permeabilities greater than approximately 10 −16m 2 produced hydrostatic pore pressure gradients. The models demonstrate that permeability inhomogeneity due to lithologic variations may exert a strong control on the magnitude and spatial distribution of excess pore pressures within thrust sheets. In addition, these models indicate that it is unlikely that fluid pressure is high everywhere in a moving thrust sheet.

Mathematical modelling of gravitational compaction and clay dehydration in thick sediment layers

SUMMARY Gravitational compaction is an important process in sedimentary basins which controls the reduction of porosity with burial depth and the development of high pore fluid pressures. Often, sediments contain hydrated, expandable clay (smectite) that can undergo a transition to a dehydrated, non-expandable clay (illite). During dehydration, structural water bound within the sheet layers of smectite is released into the pore space, which can increase the pore pressure and influence geological processes such as solute transport, hydrocarbon migration and hydrothermal fracturing. A multicomponent continuum mechanics model that accounts for Darcy's Law, Terzaghi's principle of effective stress and a thermally activated dehydration reaction is derived and solved numerically. A closed-form solution is available in the limiting case of hydrostatic pore pressure and no dehydration. The results show that excess pore-pressure development is controlled by the sedimentation parameter, the dimensionless ratio of the hydraulic conductivity to the sedimentation rate. For relatively impermeable sediments, chemically released water can increase the excess pore pressure by as much as 30 per cent, and the excess pressure persists over geological time-scales. The pressure contribution due to the excess pore water is important provided that the dehydration goes to completion at sufficient burial depth, which depends in part on the activation energy of the reaction. If sediments overlie a permeable basement, fluid can flow out of the sediments and relieve pore pressure throughout the sedimentary column.

Complex nature of stress inside loaded articular cartilage

We show that in the early stages of loading of the cartilage matrix extensive water exudation and related physicochemical and structural changes give rise to a distinctly consolidatable system. By enzymatically modifying the pre-existing osmotic condition of the normal matrix and measuring its hydrostatic excess pore pressure, we have studied the exact influence of physicochemistry on the consolidation of cartilage. We argue that the attainment of a certain minimum level of swelling stiffness of the solid skeleton, which is developed at the maximum hydrostatic excess pore pressure of the fluid, controls the effective consolidation of articular cartilage. Three related but distinct stresses are developed during cartilage deformation, namely (1) the swelling stress in the coupled proteoglycan/collagen skeleton in the early stages of deformation, (2) the hydrostatic excess pore pressure carried by the fluid component, and (3) the effective stress generated on top of the minimum value of the swelling stress in the consolidation stages following the attainment of the fluid's maximum pore pressure. The minimum value of the swelling pressure is in turn generated over and above the intrinsic osmotic pressure in the unloaded matrix. The response of the hyaluronidase-digested matrix relative to its intact state again highlights the important influence of the osmotic pressure and the coefficient of permeability, both of which are related to the volume fraction of proteoglycans on cartilage deformation, and therefore its ability to function as an effective stress-redistributing layer above the subchondral bone.

The Generalized Consolidation of Articular Cartilage: An Investigation of Its Near-Physiological Response to Static Load

This paper presents a study of the response of articular cartilage to compression whilst measuring simultaneously its strain and fluid excess pore pressure using a newly developed experimental apparatus for testing the tissue in its unconfined state. This has provided a comparison of the load-induced responses of the cartilage matrix under axial, radial and 3-D consolidation regimes. Our results demonstrate that the patterns of the hydrostatic excess pore pressure for axial and 3-D consolidation are similar, but differ significantly from that obtained under the more physiologically relevant condition in which the matrix exhibits radial consolidation when loaded either through a non-porous polished stainless steel indenter or an opposing cartilage disc. Based on the transient strain characteristics obtained under axial and unconfined compression we argue that consolidation is indeed the controlling mechanism of cartilage biomechanical function.

Stress field constraints on intraplate seismicity in eastern North America

Focal mechanisms of 32 North American midplate earthquakes (mb = 3.8–6.5) were evaluated to determine if slip is compatible with a broad‐scale regional stress field derived from plate‐driving forces and, if so, under what conditions (stress regime, pore pressure, and frictional coefficient). Using independent information on in situ stress orientations from well bore breakout and hydraulic fracturing data and assuming that the regional principal stresses are in approximately horizontal and vertical planes (±10°), the constraint that the slip vector represents the direction of maximum resolved shear stress on the fault plane was used to calculate relative stress magnitudes defined by the parameter ϕ = (S2 ‐ S3)/(S1 ‐ S3) from the fault/stress geometry. As long as the focal mechanism has a component of oblique slip (i.e., the B axis does not coincide with the intermediate principal stress direction), this calculation identifies which of the two nodal planes is a geometrically possible slip plane (Gephart, 1985). Slip in a majority of the earthquakes (25 of 32) was found to be geometrically compatible with reactivation of favorably oriented preexisting fault planes in response to the broad‐scale uniform regional stress field. Slip in five events was clearly inconsistent with the regional stress field and appears to require a localized stress anomaly to explain the seismicity. Significantly, all five of these events occurred prior to 1970 (when many regional networks were installed), and their focal mechanisms are inconsistent with more recent solutions of nearby smaller events. The frictional likelihood of the geometrically possible slip on the selected fault planes was evaluated in the context of conventional frictional faulting theory. The ratio of shear to normal stress on the fault planes at hypocentral depth was calculated relative to an assumed regional stress field. Regional stress magnitudes were determined from (1) S1/S3 ratios based on the frictional strength of optimally oriented faults (the basis for the linear brittle portion of lithospheric strength profiles), (2) the computed relative stress magnitude (ϕ) values, and (3) a vertical principal stress assumed equal to the lithostat. Two end‐member possibilities were examined to explain the observed slip in these less than optimally oriented fault planes. First, the frictional coefficient was held constant on all faults, hydrostatic pore pressure was assumed regionally, and the fault zone pore pressure was determined. Since pore pressure is a measurable quantity with real limits in the crust (P0 &lt; S3), this end‐member case was used to determine which of the geometrically possible slip planes were frictionally likely slip planes. Alternately, pore pressure was fixed at hydrostatic everywhere, and the required relative lowered frictional coefficient of the fault zone was computed. Slip in 23 of the 25 geometrically compatible earthquakes was determined to also be frictionally likely in response to an approximately horizontal and vertical regional stress field derived from plate‐driving forces whose magnitudes are constrained by the frictional strength of optimally oriented faults (assuming hydrostatic pore pressure regionally). The conditions for slip on these 23 relatively “well‐oriented” earthquake faults were determined relative to this regional crustal strength model and require only moderate increases in pore pressure (between about 0.4–0.8 of lithostatic, hydrostatic is about 0.37 of lithostatic) or, alternately, moderate lowering (&lt;50%) of the frictional coefficient on the faults which slipped. Superlithostatic pore pressures are not required. Focal mechanisms for the two other earthquakes with slip vectors geometrically consistent with the regional stress field, however, did require pore pressures far exceeding the least principal stress (or extremely low coefficients of friction). These events may reflect either local stress rotations undetected with current sampling or poorly constrained focal mechanisms. The analysis also confirmed a roughly north to south contrast in stress regime between the central eastern United States and southeastern Canada previously inferred from a contrast in focal mechanisms between the two areas: most central eastern United States earthquakes occur in response to a strike‐slip stress regime, whereas the southeastern Canadian events require a thrust faulting stress regime. This contrast in stress regime, with a constant maximum horizontal stress orientation determined by far‐field plate‐driving forces, requires a systematic lateral variation in relative stress magnitudes. Superposition of stresses due to simple flexural models of glacial rebound stresses are of the correct sense to explain the observed lateral variation, but maximum computed rebound‐related stress magnitude changes are quite small (about 10 MPa) and do not appear large enough to account for the stress regime change if commonly assumed stress magnitudes determined from frictional strength apply to the crust at seismogenic depths.